From Proposals to Numbers

A stellar-mass black hole (~10 M☉) inspiralling into OC’s IMBH (8,200 M☉) produces a gravitational wave signal detectable by LISA if the mass ratio q = m/M ≥ 10−³. The SNR scales with the number of GW cycles in band. By the Peters (1964) GW-inspiral formula, a separation of a few hundredths of an AU (tens of Schwarzschild radii) merges in ~4 yr, comfortably inside LISA’s nominal mission; a wide parsec-fraction separation of 0.01 pc, by contrast, takes >10²&sup0; yr to inspiral under GW emission alone — observationally irrelevant. This is the channel that would provide a direct IMBH mass to <1%. No other channel can match LISA’s mass precision once the signal is in band. The EMRI calculator lets you vary the secondary mass, orbital separation, and eccentricity to explore the parameter space that LISA can reach in its nominal 4-year mission.

Adding more OC pulsars to the timing array reduces σ_M ∝ 1/√N_psr. The Bañares 2025 result used 5 pulsars over 5 years. To push the upper limit below 6,000 M☉ at the same significance requires either more pulsars or a longer baseline. TRAPUM (MeerKAT pulsar survey) is actively discovering new OC pulsars: each new discovery extends the array and tightens the constraint. The pulsar timing tool shows the enclosed mass sensitivity as a function of pulsar radius, timing precision, and baseline length — revealing that 15 pulsars at the same precision would halve the current upper limit, potentially pushing it below the Häberle lower bound and resolving the tension from below.

Chen et al. 2025 placed a non-detection limit at ~0.05 μJy at 3–4 μm. Deeper imaging — or a Cycle 4 follow-up at longer wavelengths, extending into the 10–20 μm range where Bondi accretion would peak for a ~8,000 M☉ IMBH — could push the Bondi mass limit below 6,000 M☉ for accretion efficiencies ε > 10−³. The JWST accretion visualiser translates a flux non-detection into a mass limit as a function of accretion efficiency and density. The key tension: the limit is efficiency-dependent, and low-efficiency (radiatively inefficient) accretion could hide an 8,200 M☉ IMBH behind the current JWST threshold.

An OC-targeted continuous-wave (CW) search using known MSP ephemerides can be run on public O4 data today. For a pulsar at 300 Hz spinning in OC’s core with a 1-year integration, the O4 ellipticity upper limit is ε < 5×10−⁷ — below the spin-down limit for most OC MSPs. A non-detection at this level constrains the dark cluster hypothesis: many spinning NSs collectively exceeding this ellipticity would produce a detectable stochastic CW background from OC’s direction. A 2-year O5 run, with its lower noise floor, pushes the limit roughly an order of magnitude lower, to ε < 5×10−⁸, further squeezing the dark-cluster parameter space. In Scenario A (with ET), the projected sensitivity reaches the spin-down limit of virtually every known OC pulsar.

The constraint stacker shows all current IMBH mass estimates and limits on a single log-mass axis. The 6,000–8,200 M☉ tension is visible: both the Häberle lower bound and the Bañares upper bound appear simultaneously. Adding the JWST accretion limit (parameter-dependent), the Chen 2025 result, and the pulsar timing data shows a cluster of constraints around 6,000–15,000 M☉ with active tension. The LISA and CW channels will eventually resolve this. In Scenario A, the stacker shows where the LISA measurement would land relative to the current spread; in Scenario B, it shows what the current data can already rule out. The stacker is the best single-page summary of the observational status.